M677459 Mersenne number exponent details

is 2 ⁶⁷⁷⁴⁵⁹ - 1

has 203936 decimal digits

takes 0.014 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	43.8608	70.1493%	1000000	30000000	0.0747	5.5366%	43.9356	71.8020%	1.6527%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	240000	0.0006	21.1635%	0.0006	60.5818%	10.5818%
GPU72	2⁴⁴	0.0000	54.5455%	11000	400000	0.0009	16.0355%	0.0009	61.8343%	7.2889%
Difference	+23	+43.8608	+15.6038%	+989000	+29600000	+0.0738	-10.4989%	+43.9346	+9.9677%	+9.9677%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
677459	140348227849617316296073	24	76.893	103584296503269804 2² × 3 × 8632024708605817	2014-03-30	4	8632024708605817	25,935	13,619,657	25,437,726

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.009	-	-	2.615%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.232%
2002-07-14T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.855%
2002-10-19T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.012	-	-	2.618%
2003-06-17T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.508%
2011-07-19T21:09:00	Jocelyn Larouche	Manual testing	330261	330261		-		-	-	0.010	-	-	1.418%
2011-09-11T15:19:00	Jocelyn Larouche	Manual testing	550436	550436		-		-	-	0.016	-	-	1.791%
2012-08-29T21:05:00	Jocelyn Larouche	Manual testing	1354918	1354918		-		-	-	0.039	-	-	2.575%
unknown			1000000	30000000		-		-	-	0.075	-	-	5.537%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.014	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.028	-	-
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.057	-	-
2008-10-13T03:46:00	Sturle Sunde	gluck.ifi	2⁵⁸	2⁵⁹		-	-	0.057	-	-
2008-10-13T04:26:00	Sturle Sunde	gluck.ifi	2⁵⁹	2⁶⁰		-	-	0.113	-	-
2010-11-16T21:46:00	Sid & Andy	Buzz	2⁶⁰	2⁶¹		-	-	0.227	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.245 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.245 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.699	0.000%
25	50000	1.346	26.016%
30	250000	0.107	89.809%
35	1000000	0.007	99.296%

ECM Summary

B1	B2	factor	curves	GHz-days
		140348227849617316296073	1	0.00000e+0
50000	5000000		280	6.297
250000	25000000		44	4.948

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-27T16:46:00	Team_Bundu	bundu1	50000	5000000						1	0.022
2007-12-04T22:27:00	James Heinrich	WHS	50000	5000000						1	0.022
2007-12-05T06:06:00	James Heinrich	WHS	50000	5000000						1	0.022
2008-03-28T03:49:00	Scott Kurowski	UW1	50000	5000000						3	0.067
2008-10-21T17:30:00	Sturle Sunde	v23	50000	5000000						3	0.067
2009-01-16T00:00:00	Sturle Sunde	v23	50000	5000000						3	0.067
2009-03-18T19:57:00	Sturle Sunde	v21	50000	5000000						3	0.067
2009-06-11T03:30:00	JPH	diablo	50000	5000000						3	0.067
2009-07-09T14:18:00	Architects Cubed	m1_41	50000	5000000						3	0.067
2009-08-24T21:59:00	Sturle Sunde	FLB-ST-0034	50000	5000000						3	0.067
2009-09-28T21:17:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2009-10-25T20:43:00	Sturle Sunde	PRE6S2CKN9ZD4EE	50000	5000000						3	0.067
2009-11-15T17:26:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2009-12-10T19:56:00	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.067
2010-01-04T06:12:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-01-25T00:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-02-10T06:44:00	James Hintz	03_122109	50000	5000000						3	0.067
2010-03-07T08:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-03-27T22:30:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.067
2010-04-17T15:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-05-07T22:57:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-06-06T19:10:00	James Hintz	18_051310	50000	5000000						3	0.067
2010-06-24T21:04:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-08-25T19:58:00	Sturle Sunde	PRE6S32KN9Z73PR	50000	5000000						3	0.067
2010-09-14T17:56:00	Sturle Sunde	000461A92481	50000	5000000						3	0.067
2010-09-28T16:42:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-10-04T19:37:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-10-21T23:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2010-11-07T16:08:00	Kamil_Górski	thefault	50000	5000000						3	0.067
2010-11-29T22:05:00	Sturle Sunde	000461A92481	50000	5000000						3	0.067
2010-12-13T17:25:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-01-04T19:26:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-01-20T04:28:00	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.067
2011-02-05T21:03:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-02-23T03:36:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-03-08T19:07:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.067
2011-03-24T15:36:00	Damian Silvestre	PcMa	50000	5000000						3	0.067
2011-05-11T19:14:00	Sturle Sunde	PRE0011254B6EE4	50000	5000000						3	0.067
2011-05-12T15:08:00	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.067
2011-05-30T00:47:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-06-20T17:52:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2011-07-20T10:42:00	Lukasz Wrobel	w-l	50000	5000000						3	0.067
2011-08-22T23:45:00	Lukasz Wrobel	w-l	50000	5000000						3	0.067
2011-10-29T15:59:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2012-01-07T21:15:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.067
2012-02-27T16:00:00	Sturle Sunde	EIK-ST-1008	50000	5000000						3	0.067
2012-05-11T05:36:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.067
2012-08-21T13:41:00	Lackó	Iroda_Laci_uj	50000	5000000						3	0.067
2012-10-26T12:37:00	Andriy Makukha	home-i5	50000	5000000						3	0.067
2013-09-24T10:19:00	lopper	Surface_staples	50000	5000000						3	0.067
2013-12-19T15:11:00	Bruce	bfc-ws	50000	5000000						3	0.067
2014-03-30T13:26:00	Bruce	snowflake			140348227849617316296073	76.893		1		1	-
2016-05-20T14:55:37	TJAOI	Manual testing	50000	5000000						42	0.945
2017-06-02T16:26:29	TJAOI	Manual testing	50000	5000000						91	2.047
2019-09-23T15:13:44	TJAOI	Manual testing	250000	25000000						44	4.948

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-02T00:00:00	ANONYMOUS	v4_computers	3970C64DDDBF8628	0.014

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T14:53:38

Oliver Kruse

GTX-3

140348227849617316296073

FC831ED35D72DD__

2017-09-28T09:45:05

Oliver Kruse

Manual testing

140348227849617316296073

FC831ED35D72DD__

2017-11-09T02:25:58

kkmrkkblmbrbk

c4.large

140348227849617316296073

FC831ED35D72DD__

2020-04-20T02:20:41

Oliver Kruse

AddPrpType5

140348227849617316296073

1EF65B9560B5AF__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1354918 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 550436 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 330261 (P-1 stage 1)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10⁰

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10²

10³

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10⁶

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TF factor-bounds graph:

2⁶⁷

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-20T02:20:41+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront